Coherence as a resource for source-independent quantum random-number generation

Measuring quantum states provides a means to generate genuine random numbers. It has been shown that genuine randomness can be obtained even with an uncharacterized source by measuring two incompatible bases [Phys. Rev. X 6, 011020 (2016)]. As coherence is the necessary source for generating randomness, we extend the scheme and propose a framework for quantum random number generation with general uncharacterized coherence resource. The previous scheme can be treated as a special case under the framework by considering a nonlinear uncertainty-relation-based coherence witness. Considering general coherence witnesses, we propose a source-independent random-number generation scheme that achieves a higher randomness generation rate. Our paper highlights the close relation between coherence and random-number generation and may shed light on designing general semi-device-independent quantum information processing protocols.

Figure 1

A quantum random-number generator can be generally decomposed into two parts: source and measurement.

Figure 2

Source-independent quantum random-number generator. The squashing model is applied to transform the input states into qubits and vacuum states. Then, a basis is chosen to measure the squashed qubits. The dashed line on the measurement side denotes that, in some schemes [11], initial random bits are needed to choose the measurement basis randomly. Note that, in some other schemes [12], a beam splitter is used to randomly select the measurement basis, which, of course, might raise the question why one should trust a beam splitter. Such kinds of discussions appeared in Ref. [11].

Figure 3

Comparison of the randomness generation rates with an input qubit state ${\rho }_A=\frac{\mathrm{I}+x{\sigma }_x+y{\sigma }_y}{2}$ with $N\to \infty ,q_z=1,\beta =1$. (a) The lower surface describes the randomness generation rate for the uncertainty-relation-based scheme $r_u$ as shown in Eq. (26), whereas the upper surface describes the randomness generation rate for the tomography-based scheme $r_t$ as shown in Eq. (27). (b) Illustration of the gap between the two schemes $r_t-r_u\ge 0$.

Figure 4

Randomness generation rate vs intensity $\mu$ with various depolarization parameters $p$. The optimal $\mu$ for $p=0$, 0.1, and 0.3 are $\mu =1.4$, 0.9, and 0.5, respectively.

Figure 5

The performance of the tomography-based SIQRNG by optimizing the basis selection parameter $q$ where we pick $p=0.1$ and have the intensity parameter $\mu$ optimized. (a) shows the optimal value of $q$ vs the number of pulses $N$. (b) illustrates the randomness generate rate $R_t^{\varepsilon }/N$ vs the number of pulses $N$.